The present invention relates to an encoder for the orthogonal transform of, for the band compression of and for the encoding of sampled signals containing components of a frequency one-third of the sampling frequency, for example, color television signals obtained by sampling at a frequency three times the color subcarrier frequency.
The orthogonal transform is widely adopted in the analysis or band compression of various kinds of signals. Typical examples of the orthogonal transform include the Fourier transform, sine transform, cosine transform, Haar transform, Hadamard transform, Karhunen-Loeve (K-L) transform and so on.
However, in the K-L transform, a convariance matrix of the transform matrix must be obtained prior to the transform. Thus, the K-L transform is not suitable for signal processing at high speed. The Fourier transform, sine transform and cosine transform provide wide application since the order of orthogonal transform may be freely selected. However, with these types of transforms the set of elements of the transform matrix is complex. Therefore, these types of transforms are not suitable for orthogonal transforms of higher order. On the other hand, in the Haar transform or Hadamard transform, the set of elements of the transform matrix is represented by 0 and .+-.1, so that the orthogonal transform of signals is very easy. For this reason, the Haar transform or Hadamard transform is conventionally widely adopted as the orthogonal transform. However, the order of the transform matrix of the Haar transform or Hadamard transform is limited to 2.sup.m (where m is a positive integer) and, does not allow the orthogonal transform of the order of 3, 6 and 9.
Various types of processing of television signals are generally performed after sampling the television signals at a sampling frequency which is four times the color subcarrier frequency fsc. As may be understood from the sampling theorem, if the signals are sampled at a frequency which is twice or more the maximum frequency of the signals, the data of the signals may not be lost. Therefore, instead of sampling at a frequency which is four times the color subcarrier frequency fsc as described above, it is possible to sample at a frequency which is three times the color subcarrier frequency. Furthermore, if the frequency three times the color subcarrier frequency fsc is used as the sampling frequency, the amount of data to be handled decreases to 3/4 as compared to the case of the sampling frequency which is four times the color subcarrier frequency. In addition, the processing speed for sampling, A/D conversion and so on can be decreased. For this reason, the signal processing system may be made simple in construction. However, as for the orthogonal transform of the signals obtained by sampling in this manner, the Haar transform or the Hadamard transform is not suitable since the order of transform is limited to 2.sup.m. In order to subject the signals sampled at a sampling frequency three times the frequency of the signals to the orthogonal transform, it is preferable to perform the orthogonal transform of degree 3n.
If the signals sampled at a frequency four times that of the signals are subjected to the orthogonal transform using an Hadamard matrix of order 4 as a coefficient, the frequency components of the signals concentrate in two particular orthogonal transform outputs and are not obtained at other orthogonal transform outputs. The band compression of the signals can be performed utilizing this fact. However, if the signals sampled at a frequency three times that of the signals are subjected to the orthogonal transform using an Hadamard matrix of degree 4 as a coefficient, the frequency components of the signals disperse in all of the orthogonal transform outputs. If the frequency components of the signals disperse in a number of orthogonal transform outputs by the orthogonal transform, the band compression of the signals may no longer be performed. Therefore, it has thus been strongly desired to develop a method and encoder for the orthogonal transform of, for the band compression and encoding of signals which are sampled at a sampling frequency three times that of the signals subjected to the orthogonal transform.